There are two main differences between the Bill of Rights and the US Constitution. One difference has to do with when and how they were created. The second difference has to do with their subject matter.
The Constitution was created by the Constitutional Convention in 1787. It was ratified by the states in 1788. The Bill of Rights is the term we use for the first 10 amendments to this new constitution. A large number of amendments were introduced to Congress in June of 1789. The ones that Congress approved were sent to the states to be voted on in August of that year. Thus, these two documents were created in different ways at different times.
The two documents are also aimed at different purposes. The main purpose of the Constitution is to set up the structure of the US government. Much of the Constitution is devoted to saying what the parts of the government are, how they are selected, and what powers they have. The Bill of Rights, by contrast, is solely concerned with saying what the national government cannot do. It is a list of rights that are specifically protected from infringement by the federal government. Thus, the Constitution is more of a positive document in that it says what the government is and what it can do while the Bill of Rights is aimed more negatively, telling the government what it cannot do.